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  • International conference dedicated

    to the 120th anniversary of

    Kazimierz Kuratowski

    September 27 October 1, 2016,

    Lviv, Ukraine

    Abstracts of Reports

  • 2

    .

  • Contents

    Abstracts of Reports 7

    Vyacheslav Babych, Topological properties of the open extension topol-ogy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

    Taras Banakh, Topological spaces with an -base . . . . . . . . . . 8

    Taras Banakh, Adam Idzik, Igor Protasov, and Krzysztof Pszczo la,Isometric copies of directed trees in orientations of graphs . . . . 9

    Serhii Bardyla and Oleg Gutik, On the embeddings and closures ofthe topological -polycyclic monoid . . . . . . . . . . . . . . . . . 9

    Artur Bartoszewicz, Franciszek Prus-Wisniowski, and Jaros law Swa-czyna, On generating the classical ternary Cantorval . . . . . . 10

    Volodymyr Berezovski, Geodesic mappings onto symmetric manifolds 10

    Aleksander B laszczyk, Lattices of topologies . . . . . . . . . . . . . . 10

    Bogdan Bokalo, T. Banakh, and N. M. Kolos, On spaces of weaklydiscontinuous functions . . . . . . . . . . . . . . . . . . . . . . . 11

    Bartlomiej Bosek, A new variant of the game of cops and rober . . . 11

    Viktoria Brydun, T. Banakh, and Bogdan Bokalo, Preservation ofweakly discontinuous functions by topological functors . . . . . . 11

    Asylbek A. Chekeev and Tumar J. Kasymova, The epi-reective hullof the class all metric uniform spaces of a given weight . . . . . . 12

    Ostap Chervak, Ramsey multiplicity and Ramsey trees . . . . . . . . 15

    David Chodounsky, Covering properties of lters and the Mathias-Prikry forcing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

    Stanis law Domoradzki and Mykhailo Zarichnyi, The Lwow period inKuratowski's life . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

    Volodymyr Gavrylkiv, Semigroups of k-linked upfamilies . . . . . . . 16

    Szymon G lab and Filip Strobin, Dense free subgroups of automorphismgroups of homogeneous partially ordered sets . . . . . . . . . . . 18

    Yaroslav Grushka, Changeable sets and their possible applications . . 19

    3

  • 4 CONTENTS

    Jaros law Grytczuk, Graph coloring problems with number theoreticavor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

    Igor Guran and Yaroslav Prytula, Sala Weinlos and her doctoral thesisin Lwow University . . . . . . . . . . . . . . . . . . . . . . . . . . 20

    Oleg Gutik, On locally compact semitopological 0-bisimple inverse-semigroups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

    Ivan Hetman and T. Banakh, Algorithmic geometric problems con-nected with a manipulator motion . . . . . . . . . . . . . . . . . 21

    Bohdana Hladysh and O. O. Prishlyak, Continuation of function, de-ned on the circle, to optimal Morse function on the surface . . . 22

    Inna Hlushak, Oleh Nykyforchyn, Almost optimal aproximations ofcapacities on metric compacta whith capacities from a closed I-convex subspace . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

    Olena Hryniv, Metrizability of compact topological pre-Cliord semi-groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

    Miroslav Husek, Lattices of uniformly continuous functions . . . . . . 26Yuriy Ishchuk, The zero-divisors graph of a matrix semigroup . . . . 26Joanna Jureczko and Ryszard Frankiewicz, On Kuratowski partitions 27Olena Karlova, Extension of Baire-one functions from countable sets 28Alexander Kharazishvili, On nite sums of periodic functions . . . . . 29Volodymyr Kiosak, On the conformal and geodesic mappings of quasi-

    Einstein spaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30Adam Krawczyk, The Banach-Mazur game for graphs . . . . . . . . . 30Tomasz Krawczyk and Bartosz Walczak, Extending partial represen-

    tations of trapezoid graphs . . . . . . . . . . . . . . . . . . . . . 30Sergiy Maksymenko, Deformations of smooth functions on compact

    surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31Kateryna Maksymyk and Oleg Gutik, On semitopological interassoci-

    ates of the bicyclic monoid . . . . . . . . . . . . . . . . . . . . . . 31Witold Marciszewski and Miko laj Krupski, On weak and pointwise

    topologies in function spaces . . . . . . . . . . . . . . . . . . . . . 33Vita Markitan, Q-representation of real numbers determined by an

    innite double stochastic matrices and sets associated with them 33Tetiana Martynyuk, T. Banakh, O. Chervak, A. Ravsky, and M. Simkiv,

    Kuratowski monoids of n-topological spaces . . . . . . . . . . . . 34Volodymyr Maslyuchenko, Contribution of K. Kuratowski to the the-

    ory of separately continuous functions . . . . . . . . . . . . . . . 34Vasyl Melnyk and Volodymyr Maslyuchenko, The development of

    Hahn's theorem on an intermediate function . . . . . . . . . . . . 36Daria Michalik, Cones of locally connected curves . . . . . . . . . . . 38Volodymyr Mykhaylyuk, Continuous extension from countable sets . . 38

  • CONTENTS 5

    Andrzej Nagorko and G. C. Bell, On stability of asymptotic proper-ty C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

    Pawe l Naroski, Pawe l Rzazewski, and Ma lgorzata Sleszynska-Nowak,Localization in graphs with colored edges . . . . . . . . . . . . . 40

    Vasyl Nesterenko, Equi-cliquishness and the Hahn property . . . . . . 40Magdalena Nowak and Taras Banakh, Topological fractals . . . . . . 41Oleg Pikhurko, Evan DeCorte, Spherical sets avoiding a prescribed set

    of angles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41Inna Pozdniakova and Oleg Gutik, On the monoid of monotone injec-

    tive partial selfmaps of N N with conite domains and images . 42Alexander Prishlyak, Topology of ows with a xed point on the

    boundary of 2-manifold . . . . . . . . . . . . . . . . . . . . . . . 42Anatolij K. Prykarpatsky, Denis L. Blackmore, and Orest D. Arte-

    movych, Hamilton operators and related integrable dierential-algebraic Novikov-Leibniz structures . . . . . . . . . . . . . . . . 43

    Yaroslav Prytula, Kazimierz Kuratowski and his Lviv students . . . . 44Taras Radul, Max-Plus convex compacta: a categorical approach . . 44Robert Ra lowski and Aleksander Cieslak, Nonmeasurable images in

    Polish space with respect to selected sigma ideals . . . . . . . . . 45Menachem Shlossberg, Michael Megrelishvili and Luie Polev, Mini-

    mality of the semidirect product . . . . . . . . . . . . . . . . . . 45Markiyan Simkiv and Taras Banakh, Interplay between dimensions of

    micro- and macro-fractals . . . . . . . . . . . . . . . . . . . . . . 46Ol'ga Sipacheva and E. Reznichenko, Discrete subsets in topological

    groups and countable extremally disconnected groups . . . . . . 46Arkadiy Skopenkov, Sergey Avvakumov, Isaac Mabillard, and Uli Wag-

    ner, Eliminating Higher-Multiplicity Intersections, III. Codimen-sion 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

    Oleksandra Sobol and Oleg Gutik, Feebly compact topologies on thesemilattice expn . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

    Yuliia Soroka, Homeotopy groups of non-singular foliations on theplane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

    Filip Strobin, Marek Balcerzak, and Ehrhard Behrends, On certainuniformly open multilinear mappings . . . . . . . . . . . . . . . . 49

    Paul Szeptycki and Rodrigo Hernandez-Gutierrez, Uniform powers ofcompacta and the proximal game . . . . . . . . . . . . . . . . . . 50

    Piotr Szewczak and Boaz Tsaban, Productively (and non-productively)Menger spaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

    Henryk Torunczyk, Selected mathematical achievements of KazimierzKuratowski . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

    Iryna Tytar, Periodic Fibonacci words . . . . . . . . . . . . . . . . . 52

  • 6 International conference dedicated to the 120th anniversary of K. Kuratowski

    Myroslava Vovk, I. Banakh, and T. Banakh, An example of a non-Borel locally-connected nite-dimensional topological group . . . 52

    Tomasz Weiss, Translations of sets that belong to the ideal of meagernull sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

    Alexander Wol, Steven Chaplick, Krzysztof Fleszar, Fabian Lipp, OlegVerbitsky, and Alex Ravsky, Drawing graphs on few lines and fewplanes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

    Piotr Zakrzewski and Roman Pol, Homogeneity properties of a -idealrelated to a Borel measure . . . . . . . . . . . . . . . . . . . . . . 54

    Mykhailo Zarichnyi and Lidiya Bazylevych, Hyperspaces of compactconvex sets: some new results . . . . . . . . . . . . . . . . . . . . 54

    Yuri Zelinskii, Some open topological problems in analysis . . . . . . 55Szymon Zeberski, Roger B. Eggleton, Micha l Morayne, and Robert

    Ra lowski, On midpoint-free subsets of some topological groups . 56

    Index 57

  • Abstracts of Reports

    Topological properties of the open extensiontopology

    Vyacheslav Babych

    Taras Shevchenko National University of Kyiv, Kyiv, Ukraine

    vyacheslav.babych@gmail.com

    Open extension topology is introduced in [1] for the case when its carrierdiers from the one of the starting topological space by one point. A particularcase of this construction is excluded point topology which appears as an openextension of the discrete topology. The most famous example of excluded pointtopology is the Sierpinski space. We study topological properties of the gener-alization of this construction to the case of an arbitrary superset of the carrierof the original spa